Question

Consider an elementary reaction: \[ A(g) + B(g) \rightarrow C(g) + D(g) \] If the volume of the reaction mixture is suddenly reduced to \( \frac{1}{3} \) of its initial volume, the reaction rate will become \( x \) times of the original reaction rate. The value of \( x \) is:

• A. \( \frac{1}{9} \)
• B. 9
• C. 3
• D. \( \frac{1}{3} \)

Hint:

In elementary reactions, the rate depends on the concentration of reactants. When the volume is reduced, the concentration increases, which leads to an increase in the rate, depending on the order of the reaction.

Answer 1

The Correct Option is B

For an elementary reaction, the reaction rate is directly proportional to the reactant concentrations. For a reaction with stoichiometric coefficients of 1 for both A and B, the rate law is given by: \[ {Rate} = k[A][B] \] where \( k \) represents the rate constant, and \( [A] \) and \( [B] \) denote the concentrations of reactants A and B, respectively. When the reaction mixture's volume is decreased to \( \frac{1}{3} \) of its initial volume, the reactant concentrations will triple, as concentration is inversely proportional to volume. Given that the rate is directly proportional to the product of the concentrations of A and B, the reaction rate will increase by a factor of: \[ {New rate} = k(3[A])(3[B]) = 9 \times ({Original rate}) \] Consequently, the reaction rate will be 9 times the original rate. Therefore, \( x \) equals 9.